Multitype PCR branching processes
To model amplification Polymerase Chain Reaction (PCR) techniques targeting DNA sequences of several types, we introduce a multitype PCR branching process as a generalized version of the Michaelis-Menten-based branching process model introduced in Jagers-Klebaner, 2003. We establish two limit theorems extending the results of Chigansky-Jagers-Klebaner,
Chigansky, P. +3 more
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Robust Estimation in Multitype Branching Processes Based on their Asymptotic Properties [PDF]
, 2011 2000 Mathematics Subject Classification: 60J80.In this work we propose two procedures for robust estimation of the individual distributions of multitype discrete-time Galton-Watson branching processes with an increasing number of ancestors, using the ...
Atanasov, Dimitar, Stoimenova, Vessela
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Coalescence on critical and subcritical multitype branching processes
Journal of Applied Probability, 2016 AbstractConsider a d-type (d<∞) Galton–Watson branching process, conditioned on the event that there are at least k≥2 individuals in the nth generation, pick k individuals at random from the nth generation and trace their lines of descent backward in time till they meet.
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Genealogical methods for multitype branching processes with applications in biology
, 2001 Biological populations are naturally organized into lineages of reproducing particles. Multitype branching processes are a probabilistic description of such systems.
Shaw, Chad Abramson
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Conditional Distributions and Waiting Times in Multitype Branching Processes [PDF]
Advances in Applied Probability, 2013 In this paper we present novel results for discrete-time and Markovian continuous-time multitype branching processes. As a population develops, we are interested in the waiting time until a particular type of interest (such as an escape mutant) appears, and in how the distribution of individuals depends on whether this type has yet appeared ...
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Supercritical multitype branching processes: the ancestral types of typical individuals
, 2003 Georgii H-O, Baake E. Supercritical multitype branching processes: the ancestral types of typical individuals. Adv. Appl. Prob. 35 (2003), 1090-1110. 2003.For supercritical multitype branching processes in continuous time, weinvestigate the evolution of ...
Georgii, Hans-Otto, Baake, Ellen
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Using Inside-Outside Algorithm for Estimation of the Offspring Distribution in Multitype Branching Processes [PDF]
, 2010 Multitype branching processes (MTBP) model branching structures, where the nodes of the resulting tree are particles of different types. Usually such a process is not observable in the sense of the whole tree, but only as the “generation” at a given ...
Daskalova, Nina
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The demographic variation process of multitype branching random fields
, 1992 A system of particles of k types in Rd is considered, where each particle, depending on its type, migrates and lives a random amount of time, at the end of which it branches according to a multitype law.
Lopez-Mimbela, J.Alfredo +1 more
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On convergence properties of infinitesimal generators of scaled multitype CBI processes∗ [PDF]
, 2016 It is a common method for proving the weak convergence of a sequence of time-homogeneous Markov processes toward a time-homogeneous Markov process first to show the convergence of the corresponding infinitesimal generators and then to check some ...
Gyula Pap +3 more
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The multitype branching diffusion
The multitype branching diffusion (MBD) is considered. A review of the general theory of multitype point processes is given in Section 2, and spatial central limit theorems for homogeneous infinitely divisible processes are proven in Section 3.
Ivanoff, B. Gail
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